Monotone quantum stochastic processes and covariant dynamical hemigroups

Based on the Hilbert C^?-module structure we study non-stationary monotone quantum stochastic processes and general Markov processes constructed from quantum dynamical hemigroups indexed by a totally ordered set. We prove that the quantum stochastic monotone process implementing the weakly covariant process described by a covariant quantum dynamical hemigroup with respect to a symmetry semigroup is again covariant in the strong sense.     

Interaction of aluminum polyhydroxochloride sol and poly(4-vinylbenzene sulfonic acid) sodium salt

The interaction of aluminum polyhydroxochloride sol and poly(4-vinylbenzene sulfonic acid) sodium salt is studied. It is found that, in dilute aqueous solutions at pH 4.6, aluminum polyhydroxochloride sol and poly(4-vinylbenzene sulfonic acid) sodium salt form insoluble polymer-colloid complexes of steady compositions. Potentiometric titration data show that the interaction between particles of aluminum polyhy-droxochloride sol and linear macromolecules of the polyelectrolyte occurs via salt bonds formed between unlikely charged groups on the surface of particles and units of the linear polyelectrolyte. The composition of the polymer-colloid complex is determined, and the degree of conversion for the reaction of aluminum poly-hydroxochloride sol and poly(4-vinylbenzene sulfonic acid) sodium salt is estimated. The influence of various polyelectrolytes on the stability of the polymer-colloid complex is studied.     

Synthesis of trifluoromethylated heterocycles using partially fluorinated epoxides

Reaction of 2-trifluoromethyl- (1) and 2,2-bis(trifluoromethyl)- (2) oxiranes with a variety of sulfur nucleophiles proceeds rapidly and under mild conditions. For example, epoxide 2 reacts with aqueous solution of Na₂S, producing S[CH₂C(CF₃)₂OH]₂. Reaction of 2 with Na₂S₂O₃ leads to the formation of the corresponding Bunte salt. Interaction of 2 with NaSCN in water proceeds exothermically and results in high-yield formation of cyclic imine 5. Although this material can be isolated, it has limited stability and undergoes cyclotrimerization at ambient temperature, giving the corresponding 1,3,5-triazine. A number of heterocyclic compounds containing pendant -CH₂C(CF₃)₂OH group were prepared by the reaction of the corresponding thio-derivatives, such as pyridine-2-thiole with epoxide 2. It was found that fluoride anion catalyzes the reaction of epoxides 1 and 2 with isothiocyanates carrying electron withdrawing groups at nitrogen. The reaction results in nucleophilic cyclization and formation of the corresponding exocyclic imines containing a 1,3-oxothiolane moiety. Carbon disulfide was also found to be active in this process, reacting with epoxides 1 and 2 at ambient to give the corresponding trifluoromethylated 1,3-oxathiolane-2-thiones in 58-65% yield.     

Jacobi-type identities in algebras and superalgebras

We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of an arbitrary associative algebra. One is a consequence of the other (fundamental identity). From the fundamental identity, we derive a set of four identities (one of which is the Jacobi identity) represented in terms of double commutators and anticommutators. We establish that two of the four identities are independent and show that if the fundamental identity holds for an algebra, then the multiplication operation in that algebra is associative. We find a generalization of the obtained results to the super case and give a generalization of the fundamental identity in the case of arbitrary elements. For nondegenerate even symplectic (super)manifolds, we discuss analogues of the fundamental identity.     

Positive Results and Counterexamples in Comonotone Approximation

We estimate the degree of comonotone polynomial approximation of continuous functions f, on [?1,1], that change monotonicity s??1 times in the interval, when the degree of unconstrained polynomial approximation E _n (f)??n ^??? , n??1. We ask whether the degree of comonotone approximation is necessarily ??c(??,s)n ^??? , n??1, and if not, what can be said. It turns out that for each s??1, there is an exceptional set A _s of ????s for which the above estimate cannot be achieved.     

Weak antiferromagnetic ordering induced by Dzyaloshinskii-Moriya interaction and pure magnetic reflections in MnSi-type crystals

A symmetry analysis of the Dzyaloshinskii-Moriya (DM) interaction in MnSi-type crystals reveals a nontrivial antiferromagnetic pattern of tilted Mn moments remaining even after an unwinding of the ground-state helix by a strong magnetic field. The remaining tilts are caused by that component of the DM vector which is perpendicular to the component responsible for helical spiraling; both components are evaluated and related to the atomic structure using a simple model. It is shown that the tilting should induce pure magnetic reflections 00?(?=2n+1) in neutron or x-ray magnetic scattering. In addition, the DM-induced antiferromagnetic ordering is important for the core structure of intrinsic defects, for the spectra of magnetic resonances, and generally for a better understanding of spin-orbit interaction in this type of magnetics.     

The Influence of Steel Projectile Shape on its Fracture at High Strain Rates

Russian Physics Journal - The paper studies the fracture of high-strength projectiles during their interaction with a steel barrier. Three types of the projectile head are considered, namely plate,...